Uncertainty Quantification in Electrical Engineering
Stochachstic methods, surrogate modelling and robust optimization

Methods for Uncertainty Quantification

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The design of efficient electrotechnical devices requires deep insight into the device’s electromagnetic field distribution. Today, this is typically obtained by computer simulations instead of physical prototypes. On the other hand, the available input data, e.g. boundary conditions, geometry, material curves, include uncertainties, e.g. unknown errors due to measurements or lack of knowledge. The influence of these errors can be characterized by uncertainty quantification. In the mathematical models, the corresponding parameters are substituted by random variables to describe the uncertainties.

Straightforward approaches such as Monte-Carlo simulations (cf. header image) are typically computationally too expensive. More sophisticated approaches, for example Gaussian process prediction (Kriging) or the generalized Polynomial Chaos approach, allow faster convergence and hence less computational effort. However, they may be affected by the curse of dimensionality.

The research focuses on the modeling of uncertainties in the context of partial differential equations, efficient methods for the quantification and (robust) optimization.

Fuhrländer, Mona ; Schöps, Sebastian (2021):
Efficient yield optimization with limited gradient information.
Cornell University, ARXIV: 2105.07799. [Preprint].

Fuhrländer, Mona ; Schöps, Sebastian (2021):
Yield Optimization using Hybrid Gaussian Process Regression and a Genetic Multi-Objective Approach.
In: Advances in Radio Science, ISSN: 1684-9965, ARXIV: 2010.04028, forthcoming. [Article]

Georg, Niklas ; Römer, Ulrich (2020):
Conformally Mapped Polynomial Chaos Expansions for Maxwell's Source Problem with Random Input Data.
In: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, pp. 1–15, ISSN: 0894-3370, DOI: 10.1002/jnm.2776, ARXIV: 2005.05152. [Article]

Georg, Niklas ; Loukrezis, Dimitrios ; Römer, Ulrich ; Schöps, Sebastian (2020):
Enhanced adaptive surrogate models with applications in uncertainty quantification for nanoplasmonics.
In: International Journal for Uncertainty Quantification, 10, (2), pp. 165–193, ISSN: 2152-5080, DOI: 10.1615/Int.J.UncertaintyQuantification.2020031727, ARXIV: 1807.07485. [Article]

Fuhrländer, Mona ; Schöps, Sebastian (2020):
A Blackbox Yield Estimation Workflow with Gaussian Process Regression for Industrial Problems.
In: Journal of Mathematics in Industry, ISSN: 2190-5983, DOI: 10.1186/s13362-020-00093-1, ARXIV: 2003.13278. [Article]

Fuhrländer, Mona ; Georg, Niklas ; Römer, Ulrich ; Schöps, Sebastian (2020):
Yield Optimization Based on Adaptive Newton-Monte Carlo and Polynomial Surrogates.
In: International Journal for Uncertainty Quantification, 10, (4), pp. 351–373, ISSN: 2152-5080, DOI: 10.1615/Int.J.UncertaintyQuantification.2020033344, ARXIV: 1912.09908. [Article]

D'Angelo, Laura ; Bontinck, Zeger ; Schöps, Sebastian ; De Gersem, Herbert (2020):
Robust Optimization of a Permanent Magnet Synchronous Machine Considering Uncertain Driving Cycles.
In: NAFEMS – Zeitschrift für numerische Simulationsmethoden und angrenzende Gebiete, pp. 71–80, ISSN: 2311-522X. [Article]

D'Angelo, Laura ; Bontinck, Zeger ; Schöps, Sebastian ; De Gersem, Herbert (2020):
Robust Optimization of a Permanent Magnet Synchronous Machine Considering Uncertain Driving Cycles.
In: IEEE Transactions on Magnetics, 56, (2), pp. 1–5, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2952218, ARXIV: 1907.06404. [Article]

Yue, Yao ; Feng, Lihong ; Benner, Peter ; Pulch, Roland ; Schöps, Sebastian. Reduced Models and Uncertainty Quantification. In Nanoelectronic Coupled Problems Solutions, volume 29 of Mathematics in Industry, chapter 15, pages 329–346. Springer, 2019. [In Collection]

Schöps, Sebastian ; Duque, David José ; De Gersem, Herbert ; Bartel, Andreas ; Günther, Michael ; Pulch, Roland. Non-Intrusive Methods for the Cosimulation of Coupled Problems. In Nanoelectronic Coupled Problems Solutions, volume 29 of Mathematics in Industry, chapter 7, pages 131–159. Springer, 2019. [In Collection]

Pulch, Roland ; Schöps, Sebastian (2019):
Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem.
In: Progress in Industrial Mathematics at ECMI 2018, volume 30 of The European Consortium for Mathematics in Industry. Springer. ISBN: 9783030275495, DOI: 10.1007/978-3-030-27550-1_2, ARXIV: 1809.06195. [In Proceedings]

Krimm, Alexander ; Casper, Thorben ; Schöps, Sebastian ; De Gersem, Herbert ; Chamoin, Ludovic (2019):
Proper Generalized Decomposition of Parameterized Electrothermal Problems Discretized by the Finite Integration Technique.
In: IEEE Transactions on Magnetics, 55, (6), pp. 7204404, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2907223, ARXIV: 1812.06867. [Article]

Jankoski, Radoslav ; Römer, Ulrich ; Schöps, Sebastian (2019):
Stochastic modeling of magnetic hysteretic properties by using multivariate random fields.
In: International Journal for Uncertainty Quantification, 9, (1), pp. 85–102, ISSN: 2152-5080, DOI: 10.1615/Int.J.UncertaintyQuantification.2019025638. [Article]

Georg, Niklas ; Ackermann, Wolfgang ; Corno, Jacopo ; Schöps, Sebastian (2019):
Uncertainty quantification for Maxwell’s eigenproblem using isogeometric analysis and mode tracking.
In: Computer Methods in Applied Mechanics and Engineering, 350, pp. 228–244, ISSN: 0045-7825, DOI: 10.1016/j.cma.2019.03.002, ARXIV: 1802.02978. [Article]

Galetzka, Armin ; Bontinck, Zeger ; Römer, Ulrich ; Schöps, Sebastian (2019):
A multilevel Monte Carlo method for high-dimensional uncertainty quantification of low-frequency electromagnetic devices.
In: IEEE Transactions on Magnetics, 55, (8), pp. 1–12, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2911053, ARXIV: 1803.09122. [Article]

Duque, David José ; Casper, Thorben ; Schöps, Sebastian ; De Gersem, Herbert ; Römer, Ulrich ; Gillon, Renaud ; Wieers, Aarnout ; Kratochvíl, Tomáš ; Götthans, Tomáš ; Meuris, Peter. Bond Wire Models. In Nanoelectronic Coupled Problems Solutions, volume 29 of Mathematics in Industry, chapter 3, pages 46–68. Springer, 2019. [In Collection]

Loukrezis, Dimitrios ; Römer, Ulrich ; Casper, Thorben ; Schöps, Sebastian ; De Gersem, Herbert (2018):
High Dimensional Uncertainty Quantification for an Electrothermal Field Problem using Stochastic Collocation on Sparse Grids and Tensor Train Decomposition.
In: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 31, (2), pp. e2222, ISSN: 0894-3370, DOI: 10.1002/jnm.2222, ARXIV: 1610.03863. [Article]

Ion, Ion Gabriel ; Bontinck, Zeger ; Loukrezis, Dimitrios ; Römer, Ulrich ; Lass, Oliver ; Ulbrich, Stefan ; Schöps, Sebastian ; De Gersem, Herbert (2018):
Robust Shape Optimization of Electric Devices Based on Deterministic Optimization Methods and Finite Element Analysis With Affine Decomposition and Design Elements.
In: Electrical Engineering (Archiv für Elektrotechnik), 100, (4), pp. 2635–2647, ISSN: 1432-0487, DOI: 10.1007/s00202-018-0716-6, ARXIV: 1805.07060. [Article]

Bontinck, Zeger ; Lass, Oliver ; Schöps, Sebastian ; De Gersem, Herbert ; Ulbrich, Stefan ; Rain, Oliver (2018):
Robust Optimization Formulations for the Design of an Electric Machine.
In: IET Science, Measurement & Technology, 12, (8), pp. 939–948, ISSN: 1751-8822, DOI: 10.1049/iet-smt.2018.5235, ARXIV: 1712.01536. [Article]

Römer, Ulrich ; Schmidt, Christian ; van Rienen, Ursula ; Schöps, Sebastian (2017):
Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues.
In: IEEE Transactions on Magnetics, 53, (6), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2017.2668841, ARXIV: 1611.07403. [Article]

Pulch, Roland ; Bartel, Andreas ; Schöps, Sebastian (2017):
Quadrature Methods with Adjusted Grids for Stochastic Models of Coupled Problems.
In: Progress in Industrial Mathematics at ECMI 2014, volume 22 of The European Consortium for Mathematics in Industry. Springer. ISBN: 978-3-319-23413-7, DOI: 10.1007/978-3-319-23413-7. [In Proceedings]

Jankoski, Radoslav ; Römer, Ulrich ; Schöps, Sebastian (2017):
Modeling of Spatial Uncertainties in the Magnetic Reluctivity.
In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 36, (4), pp. 1151–1167, ISSN: 0332-1649, DOI: 10.1108/COMPEL-10-2016-0438, ARXIV: 1610.02796. [Article]

Galetzka, Armin ; Bontinck, Zeger ; Römer, Ulrich ; Schöps, Sebastian (2017):
Multilevel Monte Carlo Simulation of the Eddy Current Problem With Random Parameters.
In: 2017 International Applied Computational Electromagnetics Society (ACES) Symposium. IEEE. ISBN: 978-1-5090-5335-3, DOI: 10.23919/ROPACES.2017.7916062, ARXIV: 1705.08173. [In Proceedings]

Bontinck, Zeger ; Lass, Oliver ; De Gersem, Herbert ; Schöps, Sebastian (2017):
Uncertainty Quantification for a Permanent Magnet Synchronous Machine with Dynamic Rotor Eccentricity.
In: Progress in Industrial Mathematics at ECMI 2016, volume 26 of The European Consortium for Mathematics in Industry. Springer. ISBN: 978-3-319-63081-6, DOI: 10.1007/978-3-319-63082-3_77. [In Proceedings]

ter Maten, E. Jan W. ; Putek, Piotr A. ; Günther, Michael ; Pulch, Roland ; Tischendorf, Caren ; Strohm, Christian ; Schoenmaker, Wim ; Meuris, Peter ; De Smedt, Bart ; Benner, Peter ; Feng, Lihong ; Banagaaya, Nicodemus ; Yue, Yao ; Janssen, Rick ; Dohmen, Jos J. ; Tasic, Bratislav ; Deleu, Frederik ; Gillon, Renaud ; Wieers, Renaud ; Brachtendorf, Hans Georg ; Bittner, Kai ; Kratochvíl, Tomás ; Petrzela, Jirí ; Sotner, Roman ; Göthans, Tomás ; Drínovský, Jirí ; Schöps, Sebastian ; Duque, David José ; Casper, Thorben ; De Gersem, Herbert ; Römer, Ulrich ; Reynier, Pascal ; Barroul, Patrice ; Masliah, Denis ; Rousseau, Benoît (2016):
Nanoelectronic COupled Problems Solutions - nanoCOPS: Modelling, Multirate, Model Order Reduction, Uncertainty Quantification, Fast Fault Simulation.
In: Journal of Mathematics in Industry, ISSN: 2190-5983, DOI: 10.1186/s13362-016-0025-5. [Article]

Römer, Ulrich ; Schmidt, Christian ; van Rienen, Ursula ; Schöps, Sebastian (2016):
Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues.
In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). ISBN: 978-1-5090-1032-5, DOI: 10.1109/CEFC.2016.7816321, URL: http://cefc2016.org, Digest. [In Proceedings]

Römer, Ulrich ; Schöps, Sebastian ; Weiland, Thomas (2016):
Stochastic Modeling and Regularity of the Nonlinear Elliptic curl-curl Equation.
In: SIAM/ASA Journal on Uncertainty Quantification, 4, pp. 952–979, ISSN: 2166-2525, DOI: 10.1137/15M1026535, ARXIV: 1606.07643. [Article]

Jankoski, Radoslav ; Römer, Ulrich ; Schöps, Sebastian (2016):
Stochastic Modeling of an Inhomogeneous Magnetic Reluctivity Using the Karhunen-Loève Expansion and the Hierarchical Matrix Technique.
In: XXIV Symposium Electromagnetic Phenomena in Nonlinear Circuits – Proceedings EPNC 2016. Poznań, PTETiS Publishers. ISBN: 9788362712045. [In Proceedings]

Casper, Thorben ; Römer, Ulrich ; Schöps, Sebastian (2016):
Determination of Bond Wire Failure Probabilities in Microelectronic Packages.
In: 22nd International Workshop on Thermal Investigations of ICs and Systems (THERMINIC 2016), 39–44. IEEE. ISBN: 978-1-5090-5450-3, DOI: 10.1109/THERMINIC.2016.7748645, ARXIV: 1609.06187. [In Proceedings]

Casper, Thorben ; De Gersem, Herbert ; Gillon, Renaud ; Götthans, Tomáš ; Kratochvíl, Tomáš ; Meuris, Peter ; Schöps, Sebastian (2016):
Electrothermal Simulation of Bonding Wire Degradation under Uncertain Geometries.
In: Proceedings of the 2016 Design, Automation & Test in Europe Conference & Exhibition (DATE), 1297–1302. IEEE. ISBN: 978-3-9815370-6-2, URL: http://www.date-conference.com, ARXIV: 1610.04303. [In Proceedings]

Bontinck, Zeger ; Lass, Oliver ; De Gersem, Herbert ; Schöps, Sebastian (2016):
UQ of a PMSM With Dynamic Rotor Eccentricity and Shape Optimization of its Magnets.
In: XXIV Symposium Electromagnetic Phenomena in Nonlinear Circuits – Proceedings EPNC 2016, 81–82. Poznań, PTETiS Publishers. ISBN: 9788362712045. [In Proceedings]

Bontinck, Zeger ; De Gersem, Herbert ; Schöps, Sebastian (2016):
Response Surface Models for the Uncertainty Quantification of Eccentric Permanent Magnet Synchronous Machines.
In: IEEE Transactions on Magnetics, ISSN: 0018-9464, DOI: 10.1109/TMAG.2015.2491607, Article #7203404. [Article]

Römer, Ulrich ; Schöps, Sebastian (2015):
Adjoint Error Estimation for a Pseudo-Spectral Approach to Stochastic Field-Circuit Coupled Problems.
In: Proceedings in Applied Mathematics and Mechanics, volume 15, 711–714. Wiley. DOI: 10.1002/pamm.201510345. [In Proceedings]

Römer, Ulrich ; Schöps, Sebastian ; De Gersem, Herbert (2015):
An Adjoint Approach for Uncertainty Quantification of Magnetoquasistatic Field Problems.
In: Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA) 2015, 887–890. IEEE. ISBN: 978-1-4799-7805-2, DOI: 10.1109/ICEAA.2015.7297241. [In Proceedings]

Römer, Ulrich ; Casper, Thorben ; Pulch, Roland ; ter Maten, E. Jan W. (2015):
Algorithm for computation of failure probabilities and ageing effects.
nanoCOPS FP7-ICT-2013-11/619166, D2.6. [Report].

Pulch, Roland ; Putek, Piotr ; Schöps, Sebastian ; Yue, Yao ; ter Maten, E. Jan W. (2015):
Algorithm using Polynomial Chaos and reduced-order models in co-simulation of coupled problems with random parameters.
nanoCOPS FP7-ICT-2013-11/619166, D2.5. [Report].

Dölz, Jürgen ; Harbrecht, Helmut ; Peters, Michael (2015):
$\mathcal H$-matrix accelerated second moment analysis for potentials with rough correlation.
In: Journal of Scientific Computing, 65, (1), pp. 387–410. [Article]

Corno, Jacopo ; de Falco, Carlo ; De Gersem, Herbert ; Schöps, Sebastian (2015):
Isogeometric Analysis Simulation of TESLA Cavities Under Uncertainty.
In: Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA) 2015, 1508–1511. IEEE. ISBN: 978-1-4799-7805-2, DOI: 10.1109/ICEAA.2015.7297375, ARXIV: 1711.01828. [In Proceedings]

Römer, Ulrich ; Schöps, Sebastian ; Weiland, Thomas (2014):
Approximation of Moments for the Nonlinear Magnetoquasistatics Problem with Material Uncertainties.
In: IEEE Transactions on Magnetics, 50, (2), pp. 417–420, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2284637. [Article]

Bontinck, Zeger ; De Gersem, Herbert ; Schöps, Sebastian (2014):
Uncertainty Quantification of the Eccentricity of Permanent Magnetic Synchronous Machines.
In: XXIII Symposium Electromagnetic Phenomena in Nonlinear Circuits – Proceedings EPNC 2014. PTETiS Publishers. ISBN: 978-83-62712-00-7. [In Proceedings]

Bartel, Andreas ; De Gersem, Herbert ; Hülsmann, Timo ; Römer, Ulrich ; Schöps, Sebastian ; Weiland, Thomas (2013):
Quantification of Uncertainty in the Field Quality of Magnets Originating from Material Measurements.
In: IEEE Transactions on Magnetics, 49, (5), pp. 2367–2370, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2241041. [Article]